Multi-objective optimal design of multiple dependent state sampling plan for over-dispersed data under the condition on a new zero-inflated distribution

A sampling plan can help to determine the quality of products, monitor the goodness of materials, and validate whether the yields are free from defects. When the manufacturing process is precisely aligned, defects are minimized during sampling inspection. This study proposed a multiple dependent state (MDS) sampling plan under a zero-inflated Poisson quasi-Lindley (ZIPQL) distribution, denoted by MDSZIPQL to count zero-inflated data. A genetic algorithm with multi-objective optimization was used to estimate the optimal plan parameters to maximize the probability of accepting a lot (Pa) and minimize the total cost of inspection (TC) and the average sample number (ASN) simultaneously. A sensitivity analysis of the required sample size assessed the performance of the proposed MDSZIPQL as numerical examples compared to the MDS plan under a zero-inflated Poisson (MDSZIP) distribution. Simulation study results found that the required sample sizes and ASN of the MDSZIPQL plan were less than the MDSZIP plan, indicating that the MDSZIPQL plan performed better than the MDSZIP plan regarding the required sample size and ASN. Two real data sets were illustrated under the proposed MDSZIPQL plan and compared to the MDSZIP plan. Results showed that the MDSZIPQL plan had a smaller number of required sample sizes, ASN value and TC value than the MDSZIP plan (or maximum value of Pa). Therefore, the proposed MDSZIPQL plan was more efficient than the existing MDSZIP plan